The current implementation only deals with spherical water
droplets, but the algorithm could be modified to produce effects that
result from particles of other shapes, such as halos resulting from
crystalline shapes, as described in Rainbows, Haloes, and Glories [ 1].
The directional lookup table described in part 2 would need to be
recomputed to account for the different geometry, and the directional lookup would possibly need to be expanded to a higher dimension if the desired effect did not occur in a 1-dimensional angular
space, as is the case with rainbows.
Another possibility would be to create a volumetric photon map-ping-based version of the multiple-scattering path tracing integrator.
Photon mapping is a technique developed by Henrik Jensen in which
virtual “photons” are sent from the light into the scene and stored in a
tree structure when they reach a certain termination criteria [ 5]. The
renderer literally shines light on the scene and stores where it hits.
Then, in the rendering phase, the camera “collects” photons near the
rays that it sends into the scene, producing results that, while not physically correct, have low noise. Another technique to try would be a bidirectional path tracer as proposed by Lafortune and Willems [ 6]. With
bidirectional path tracing, sub-paths are traced both from the camera
and from the light. Paths from the light or camera side that make small
contributions to the resulting image can be ignored; essentially, importance sampling is performed on the sub-paths. Then, the sub-paths can
be combined, and the result is an image with considerably less variance.
Thanks to Qiqi Wang for providing the volumetric dataset and algorithm for tracing through unstructured meshes. Also, thanks to Pat
Hanrahan for providing support and advice on this project.
1. Greenler, R. 1990. Rainbows, Halos, and Glories. Cambridge University Press, Cambridge, UK.
2. Hanrahan, P. Law of reflection. https://graphics.stanford.edu/
3. Huibers, P. 1997. Models for the wavelength dependence of the index of refraction of water. Appl. Optics 36, 16.
4. Humphreys, G. and Pharr, M. 2004. Physically Based Rendering.
Elsevier, San Francisco, CA.
5. Jensen, H. 2001. Realistic Image Synthesis Using Photon Mapping.
AK Peters, Wellesley, MA.
6. Lafortune, E. and Willems, Y. D. 1993. Bi-directional path-tracing.
In Proceedings of ACM Compugraphics. Alvor, Portugal. 145-153.
7. Nave, R. Fresnel’s Equations. http://hyperphysics.phy-astr.gsu.edu/
8. Weisstein, E. Snell’s law. http://scienceworld.wolfram.com/
James Hegarty ( email@example.com) is a sophomore at Stanford
University. He enjoys photography, playing guitar, and conducting
computer graphics research.
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